The South Carolina Republican — who has repeatedly denounced Moore since sexual misconduct allegations against the Alabama candidate first surfaced last month — said any Republican will be asked repeatedly about Moore.

"Roy Moore will be the gift that keeps on giving for the Democrats," he said Monday during a CNN interview. "It will define the 2018 election... To think you can elect Roy Moore without getting the baggage of Roy Moore is pretty naive."

Moore has been accused of abusing, assaulting and harassing teenagers — one as young as 14 — while he was in his 30s. He has denied the allegations.

When the accusations first came to light, Republicans called on Moore to step aside from the campaign if the allegations were true. But as Moore has forged on, they have walked back their criticism, like Senate Majority Leader Mitch McConnell, who has said the race is up for the people of Alabama to decide.

Graham noted that if Moore wins, there will be a Senate Ethics Committee investigation into the allegations against him.

"If the ethics committee, in a bipartisan manner, supports the allegations that he, in fact, a child molester, then my view is that's inconsistent with being a member of the body," Graham said. "But there'll be due process offered Mr. Moore if he wins."